A Uniform Theory of Conditionals: Beyond Stalnaker - Will Starr

Stalnaker on the Direct Argument Two Kinds of Conditionals Stalnaker’s Analysis A New Analysis References 


Outline 

A Uniform Theory of Conditionals 

Stalnaker and Beyond 

William Starr 

03.05.12 

1 Stalnaker on the Direct Argument 

2 Two Kinds of Conditionals 

3 Stalnaker’s Analysis 

4 A New Analysis 

William Starr | A Uniform Theory of Conditionals | Modality Seminar | Cornell University 1/69 



The Direct Argument 

Conditional to Disjunction 

The Direct Argument (DA) 

Yet: 

1 It is uncontroversial that (2) follows from (1) 

(1) If the butler didn’t do it, the gardener did 

(2) Either the butler or the gardener did it 

2 But, (1) also seems to follow from (2) 

3 Then if A then B and not A or B are equivalent 

4 So indicative conditionals are material conditionals 

• Material conditional analysis of indicatives is terrible! 

• ¬φ φ ⊃ φ, ¬(φ ⊃ ψ) φ 


Stalnaker (1975) 

Uniform Theory of Conditionals and Response to Direct Argument 

• Stalnaker: the similarity analysis of subjunctive 

conditionals works for indicatives too 

• To make it work, he relies on some ideas about how 

context and inference work 

• Context: a set of possible worlds 

• Inference: needn’t always be captured semantically, 

sometimes it makes use of context 

• Call these reasonable inferences 

• Using these ideas he makes the similarity analysis of 

indicative plausible 

• But he also responds to the direct argument: 

disjunctions do not entail indicative conditionals 

• Yet, it is often reasonable to infer one from the other 


William Starr | A Uniform Theory of Conditionals | Modality Seminar | Cornell University 5/69


Stalnaker on Context 

A Set of Possible Worlds c 


Stalnaker on Context and Assertion 

Shinking c 

• Context: the common assumptions of the 

conversational participants 

• This is information the speaker can expect her 

interlocutors to use to interpret her utterances 

• These assumptions needn’t be true, nor actual beliefs 

• This common information can be thought of as a set of 

possible worlds 

• The set of worlds not ruled out by the common 

assumptions 

• The conversationally ‘live’ possibilities 

• Successful assertions change the shared assumptions of 

the conversationalists 

• Therefore, they must change c too 

• How should we change c to reflect that a new 

proposition p has been accepted? 

• Eliminate all the worlds in c that incompatible with p: 

• c ′ = c ∩ p 

• This shrinks the set of live possibilities 

• Stalnaker calls this the context set c 




Stalnaker on Reasonable Inference 

Context Changes During an Inference 

• For A to semantically entail B: 

• Every world in which A is true, B must be true 

• But on Stalnaker’s model of context, sometimes we 

ignore certain worlds 

• Worlds outside c 

• Sometimes A may not entail B but it may be 

reasonable to infer B from A in c 

Reasonable Inference 

The inference from A to B is reasonable in c iff 

c ′ = A c ∩ c, and c ′ ⊆ B c ′ 

• The proposition expressed by A in c, together with c 

entails the proposition expressed by B in c ∩ A c 


Stalnaker’s Uniform Analysis 

Overview and Semantics 

• Stalnaker’s tact: give a semantics for (if φ) ψ that is 

plausible for both indicatives and subjunctives 

• Maintain that indicatives and subjunctives have 

identical semantics, but differ pragmatically 

Semantics for Both Varieties (Stalnaker 1968, 1975) 

1 (if φ) ψ is true at w if and only if ψ is true at all of the 

φ-worlds most similar to w 

2 (if φ) ψ f = {w | f(w, φ f ) ⊆ ψ f } 

• f(w, φ f ): the set of φ-worlds most similar to w 

• f obeys three constraints, e.g. f(w, p) ⊆ p 





The Pragmatics of Indicatives 


Stalnaker on Disjunction 

Appropriateness Conditions 

Pragmatics for Indicatives (Stalnaker 1975: 69) 

1 (if φ) ψ is true in c at w ∈ c iff: 

• ψ is true at all of the φ-worlds in c most similar to w 

2 (if φ) ψ c,f = {w ∈ c | f(w, φ c,f ∩ c) ⊆ ψ c,f } 

Appropriateness of Disjunctions (Stalnaker 1975: 71) 

• Disjunctive assertions appropriate only in a context 

where either disjunct to be true without the other 

• An assertion of A ∨ B is appropriate if 

• There is a A ∧ ¬B-world in c 

• There is a ¬A ∧ B-world in c 

• Suppose we’ve ruled out the possibility that the Butler 

did it and the gardener didn’t. 

(3) ?? Either the Butler did it, or the gardener did it. 




The Direct Argument is Reasonable 

From Or to If 


Reasonable Inference 

Further Applications 

• Suppose B ∨ G is felicitously asserted in c 0 

• Then there are B ∧ ¬G and ¬B ∧ G-worlds in c 0 

• All ¬B ∧ ¬G-worlds are eliminated in 

c 1 = c 0 ∩ B ∨ G c 

• The inference to (if ¬B) G will be reasonable if 

(4) c 1 ⊆ (if ¬B) G c1 ,f 

• (if ¬B) G c1 ,f = {w ∈ c 1 | f(w, ¬B c1 ,f ∩ c 1 ) ⊆ G c1 ,f} 

• By Success ∀w : f(w, ¬B c1 ,f ∩ c 1 ) ⊆ (¬B c1 ,f ∩ c 1 ) 

• Since all of the ¬B-worlds in c 1 are G-worlds, this 

means that f(w, ¬B c1 ,f ∩ c 1 ) ⊆ G c1 ,f 

• So (if ¬B) G c1 ,f = c 1 ! 

• Condition (4) holds so, the inference is reasonable! 

• Stalnaker’s indicative semantics invalidates: 

Antecedent Strengthening A → B (A ∧ B) → C 

Disjunctive Antecedents 

(A ∨ B) → C (A → C) ∧ (B → C) 

Transitivity A → B, B → C A → C 

Contraposition A → B ¬B → ¬A 

• Yet they often sound plausible! 

• As it turns out, these are also reasonable inferences 

(w/a little tweaking) 




Two Kinds of Conditionals 

Indicative and Subjunctive 

‘Indicative’ Conditionals 

(5) a. If Bob danced, Leland danced 

b. If Bob is dancing, Leland is dancing 

‘Subjunctive’ Conditionals 

Past (looking) antecedent + modal consequent 

(6) a. If Bob had danced, Leland would have danced 

b. If Bob had danced, Leland might have danced 

c. If Bob had danced, Leland could have danced 

d. If Bob danced, Leland would dance 

e. If Bob were to dance, Leland would dance 



Felicitous After Denying Antecedent? 

(7) a. # Bob never danced. If Bob danced, Leland 

danced. 

b. # Bob isn’t dancing. If Bob is dancing, Leland is 

dancing. 

(8) a. Bob never danced. If Bob had danced, Leland 

would have danced. 

b. Bob never danced. If Bob had danced, Leland 

might have danced. 


1 Indicative conditionals? × 

2 Subjunctive conditionals? ̌ 





The Subjunctive Suggestion 


Assertions of if Bob had danced, Leland would have danced 

often suggest that Bob didn’t dance. 

• Evidence for the suggestion? 

• Infelicity of asserting that Bob did dance and then 

asserting the subjunctive conditional 

(9) # Bob definitely danced. If Bob had danced, Leland 

would have danced. 

• As discussed earlier in semester, this suggestion isn’t 

an entailment or presupposition 



Ingredients of a Subjunctive Antecedent 

(10) a. If Bob had danced, Leland would have danced 

b. If Bob were to dance, Leland would dance 

c. If Bob danced, Leland would dance 

• Antecedents: past tense look, not past meaning 

(11) Bob died yesterday. If he had died tomorrow instead, 

he would have been 98 years old. 

• Not possible w/genuine past tense had died 

(12) Yesterday I went to the Black Lodge. By the time I 

got there, Bob had died, but Cooper hadn’t. 

(13) # I will go to the Black Lodge tomorrow. By the time 

I get there, Bob had died, but Cooper hadn’t. 





Ingredients of a Subjunctive Antecedent 

• Past tense does not contribute its normal meaning in 

subjunctive antecedents 

• This is not true for indicative antecedents 

(11) Bob died yesterday. If he had died tomorrow instead, 

he would have been 98 years old. 

{ } 

was 

(14) # If Bob died tomorrow, he 

98 years old 

will be 

• So we have one more difference between the two kinds 



The Data So Far 







• Suggestion not asserted, presupposed or entailed 

Subjunctive Antecedents and Past Tense 

Unlike indicative antecedents, subjunctive ones have past 

tense morphology that does not have past tense meaning. 




Towards an Explanation 

Stalnaker’s Distinction 



Stalnaker’s Distinction: in pictures 

Stalnaker’s Distinction (Stalnaker 1975: §3) 

1 Indicative conditionals concern only antecedent worlds 

within the live possibilities c, which represent what’s 

being taken for granted in the discourse. 

2 Subjunctive conditionals concern antecedent worlds 

that may not be among c, that is they may be 

counterfactual from the perspective of the discourse. 

As Stalnaker (1975: 69) puts it “the idea [for indicative 

conditionals] is that when a speaker says if A, then 

everything he is presupposing to hold in the actual 

situation is presupposed to hold in the hypothetical 

situation in which A is true.” 

Indicatives 

c 

antecedent 

Subjunctives 

c 

antecedent 





Stalnaker’s Distinction and the Data 




• Since an indicative conditional says something about 

antecedent worlds in c, it makes sense for it to 

presuppose that there is at least one such world 

• After denying antecedent: no antecedent worlds in c 

• So indicative should be infelicitous 

• Subjunctive may reach outside c, so same reasoning 

does not apply to them 







• Suggestion not asserted, presupposed or entailed 

• Subjunctive allows antecedent worlds outside c, but 

indicative does not 

• Choosing the subjunctive over the indicative indicates 

that it is important that there are antecedent worlds 

outside c 

• One reason it may be important: antecedent is false 

• Suggestion results from strategic reasoning 






Subjunctive Antecedents and Past Tense 

Unlike indicative antecedents, subjunctive ones have past 

tense morphology that does not have past tense meaning. 

Modal Hypothesis (Isard 1974; Lyons 1977; Iatridou 2000) 

1 Past tense in subjunctive antecedents serves a modal 

function rather than a temporal one: locates 

antecedent event among a set of possibilities that may 

contain counterfactual ones. 

2 Past tense morphology serves purely temporal function 

in indicative antecedents, so they remain concerned 

with the live contextual possibilities. 



Linguistic Encoding of Stalnaker’s Distinction 

• The Modal Hypothesis explains: 

1 Why fake past tense behavior correlates w/indicative 

vs. subjunctive 

2 How Stalnaker’s Distinction is linguistically encoded 

• Suppose we follow the Modal Hypothesis 

• Then we should be able to take our indicative 

semantics for q if p and add modal operator to 

antecedent to get our semantics for subjunctives 

• Indicative: (if φ) ψ 

• Subjunctive: (if ✁φ) ψ 

• Bittner (2010: 2): subjunctives and indicatives in 

Kalaallisut are identical except that the former contain 

a modal particle in their antecedents and consequents 





Overview and Semantics 




• Stalnaker’s tact: give a semantics for (if φ) ψ that is 

plausible for both indicatives and subjunctives 

• Maintain that indicatives and subjunctives have 

identical semantics, but differ pragmatically 

Semantics for Both Varieties (Stalnaker 1968, 1975) 

1 (if φ) ψ is true at w if and only if ψ is true at all of the 

φ-worlds most similar to w 

2 (if φ) ψ f = {w | f(w, φ f ) ⊆ ψ f } 

• f(w, φ f ): the set of φ-worlds most similar to w 

• f obeys three constraints, e.g. f(w, p) ⊆ p 

Pragmatics for Indicatives (Stalnaker 1975: 69) 

1 (if φ) ψ is true in c at w iff: 

• If w ∈ c, ψ is true at all of the φ-worlds in c most 

similar to w 

2 (if φ) ψ c,f = {w ∈ c | f(w, φ c,f ∩ c) ⊆ ψ c,f } 

• Antecedent worlds f(w, φ c,f ∩ c) are all within c! 




Problem 1 

Worlds Outside c 



The Pragmatics of Indicatives, Take 2 

(if φ) ψ c,f = {w ∈ c | f(w, φ c,f ∩ c) ⊆ ψ c,f } 

• This analysis predicts that what we assert with 

indicative conditionals is false at every world outside c 

• So, suppose you rightly assert if the light in the next 

room is on, then it isn’t off 

• But it turns out we were falsely assuming for the 

purposes of our conversation that time is absolute 

• Then the actual world isn’t in c 

• Then what you said is actually false! 

Pragmatics for Indicatives: a second chance? 


• ψ is true at all of the φ-worlds in c most similar to w 

2 (if φ) ψ c,f = {w | f(w, φ c,f ∩ c) ⊆ ψ c,f } 

• We’ve eliminated the restriction to worlds in c 

• Antecedent worlds f(w, φ c,f ∩ c) are all within c! 




Another Problem 

With Modus Ponens 

Problem: Modus Ponens for Indicative Assertions Goes Invalid 

• Let w /∈ c be a φ ∧ ¬ψ-world. 

• Let ψ be true at all of the φ-worlds in c most similar to 

w: f(w, φ c,f ∩ c) ⊆ ψ c,f . 

• So the conditional proposition expressed is true at w, 

but w is a world where φ ∧ ¬ψ! 

• So the consequent doesn’t follow from the conditional 

and its antecedent. 





Pragmatics for Indicatives: a third chance? 


(i) If w ∈ c, ψ is true at all of the φ-worlds in c most 

similar to w 

(ii) If w /∈ c, ψ is simply true at all of the φ-worlds which 

are most similar to w 

2 (if φ) ψ c,f = {w | f(w, φ c,f ∩ c) ⊆ ψ c,f if w ∈ c 

& f(w, φ c,f ) ⊆ ψ c,f if w /∈ c} 

• Antecedent worlds: f(w, φ c,f ∩ c) ∪ f(w, φ c,f ) 

• Maybe what Stalnaker (1975: 69) intended? 

• But: It would allow c (if φ) ψ c,f , but we needed 

this fact in Stalnaker’s reply to the Direct Argument 



More Definitions, More Problems 

Stalnaker’s Distinction Violated 

Stalnaker’s Distinction 

1 Indicative conditionals concern only antecedent worlds 

within the live possibilities c, which represent what’s 

being taken for granted in the discourse. 

Modified Stalnaker’s (1975: 69) semantics and pragmatics: 

• Antecedent worlds: f(w, φ c,f ∩ c) ∪ f(w, φ c,f ) 

• Not a subset of c! Only those in the left set are! 

• But then we have no account of the contrasts 

Stalnaker’s distinction was supposed to explain! 


Another Problem for Stalnaker Analysis 

Incompatible with the Modal Hypothesis 

• The Modal Hypothesis explains: 

1 Why fake past tense parallels indicative/subjunctive 

2 How Stalnaker’s Distinction is linguistically encoded 

• To get subjunctive semantics, take indicative semantics 

for q if p and add modal operator to antecedent 

• Indicative: (if φ) ψ, Subjunctive: (if ✁φ) ψ 

• (if φ) ψ limited to φ worlds in c 

• Semantics of ✁φ: allow φ worlds outside c 

• Not possible w/Stalnaker’s semantics: 

• (if φ) ψ already allows φ worlds outside c, so that 

can’t be what ✁ is doing 

• So Stalnaker’s analysis cannot enjoy the benefits of 

endorsing the Modal Hypothesis 





What is the Analysis Anyway? 

The Pragmatic Constraint? (Stalnaker 2005: n.13) 

Both kinds of conditionals. . . have the same abstract semantics, but a 

context-dependent parameter of the interpretation — the selection function — is 

differently constrained by the different grammatical constructions. So, on this 

theory, the difference between the two kinds of conditionals is a semantic 

difference in two different senses, but a purely pragmatic difference in a third 

sense. The difference is semantic, first in the sense that there will normally be a 

difference in the proposition expressed by the contrasting conditional sentences, 

even when uttered in similar situations. And it is semantic also in the sense that 

the difference is marked by a conventional linguistic device (the 

tense/aspect/mood difference). But the distinction is pragmatic in that the device 

works by the way it constrains features of the context. The semantic rule that 

gives the truth conditions of the conditional as a function of the contextual 

parameter will be the same for both kinds of conditionals. 



Summary 

1 Either gives bad truth-conditions, invalidates modus 

ponens or doesn’t embody Stalnaker’s Distinction 

• But we would like a theory that does embody that 

distinction! 

2 When modified to embody Stalnaker’s Distinction, MP 

is violated 

3 Incompatible with attractive hypothesis about how 

Stalnaker’s Distinction is linguistically encoded 

• Fails entirely to explain correlation between fake past 

tense and indicative/subjunctive behavior 

4 Way forward: (if φ) ψ limited to φ worlds in c, but ✁φ 

allows φ worlds outside c in (if ✁φ) ψ 




Information Change and Semantics 

Two Views 


Information 

The Convenient Model Meets a Different Kind of Semantics 

• Everybody agrees that conversation takes place against 

an ever-changing background of information 

• Call it c for the contextual possibilities/info 

• Classic models: Stalnaker (1978), Lewis (1979) 

Classical Picture Semantics delivers propositions and 

pragmatics provides rules for changing 

background information (Stalnaker) 

Dynamic Picture Semantics operates directly on background 

information 

In Short: meaning is information vs. meaning is 

information change potential 

Informational Dynamic Semantics 

1 Assign each φ a function [φ] characterizing how it 

changes the information embodied by c: c[φ] = c ′ 

2 Think of this information as a way of tracking the 

agent’s current state of mind 

3 [φ] is the characteristic role that φ plays in changing 

an agent’s mental states 

Formal Inspirations: Pratt (1976); Heim (1982); Veltman (1996) 





For Epistemic Might (Veltman 1996) 




• c[Might(Cube)] = {w ∈ c | c[Cube] ≠ ∅} ‘Test’ 

= c or ∅ 

• c = {w 1 , w 4 }[Might(Cube)] = ? 

• {w 1 , w 4 }[Cube] = 

• c[Might(Cube)] = {w ∈ c | c[Cube] ≠ ∅} 

• c = {w 1 , w 4 }[Might(Cube)] = ? 

• {w 1 , w 4 }[Cube] = {w 1 } ≠ ∅ 

w 1 w 4 

w 1 

c 








Semantic Concepts 

• c[Might(Cube)] = {w ∈ c | c[Cube] ≠ ∅} 

• c = {w 1 , w 4 }[Might(Cube)] = c 

• {w 1 , w 4 }[Cube] = {w 1 } ≠ ∅ 

Support 

c φ ⇐⇒ c[φ] = c 

Entailment 

φ 1 , . . . , φ n ψ ⇐⇒ c[φ 1 ] · · · [φ n ] ψ 

Truth in w (Starr 2010: Ch.1) 

w φ ⇐⇒ {w}[φ] = {w} 

w 1 w 4 

c ′ = c 

Propositions 

φ = {w | w φ} 




A New Analysis 

The Semantics of Conditionals 

• Dynamic semantics: c[φ] = c ′ (Veltman 1996) 

• c[A] = {w ∈ c | w(A) = 1}, c[A ∧ B] = c[A][B], 

c[A ∨ B] = c[A] ∪ c[B], c[¬A] = c − c[A] 

The Basic Analysis (Gillies 2009; Starr 2010: Ch.2) 

• Test that all φ-worlds in c are ψ worlds: c[φ][ψ] = c[φ] 

• If yes, return c; if not, return ∅ 

• Presuppose that φ is consistent with c: c[φ] ≠ ∅ 

{ {w ∈ c | c[φ][ψ] = c[φ]} if c[φ] ≠ ∅ 

c[(if φ) ψ] = 

Undefined 

otherwise 

• Note: test concerns only antecedent worlds within c 



Motivating The Basic Analysis 

• This provides an improved logic for indicative 

conditionals (Starr 2010: Ch.2); Stalnaker invalidates: 

Import-Export A → (B → C) 

 

(A ∧ B) → C 

Antecedent Strengthening A → B (A ∧ B) → C 

Disjunctive Antecedents (A ∨ B) → C (A → C) ∧ (B → C) 

Transitivity A → B, B → C A → C 

Contraposition A → B ¬B → ¬A 

Entailment (Dynamic Strawson Entailment) 

φ 1 , . . . , φ n ψ ⇔ ∀c : c[φ 1 ] · · · [φ n ] ψ 

if c[φ 1 ] · · · [φ n ][ψ] is defined 





Extending the Basic Analysis: give a semantics for ✁φ 

What ✁φ Should Do 

Given c, ✁φ delivers a set c ′ of φ-worlds that may not be 

included in c. Under a Lewis-Stalnaker analysis, this set is 

calculated as follows. Look at each world w in c. If w is an 

φ-world it is allowed into c ′ . If w is not a φ-world, the 

φ-worlds most similar to w are placed into c ′ instead of w. 

These worlds need not come from c. 

Semantics for ✁φ 

Let f be a selection function:: 

c f [✁φ] = {w ′ | ∃w ∈ c : w ′ ∈ f(w, φ)} f 



Picturing Semantics for ✁α 

α 

c f [⊳α] 

Figure: Relationship between α, c f and c f [✁α] 

• Since ✁ has same syntax as tense, it shouldn’t be 

scoping over logically complex sentences; so α is atomic 

• In general, the expanded worlds may come from 

outside c, ∃f: c f [✁α] c f ; Stalnaker’s Distinction ̌ 

c f 





Contrast When Antecedent is Denied: Indicatives 

(7) # Bob never danced. If Bob danced, Leland danced. 

(7 ′ ) # ¬B. (if B) L 

{ {w ∈ c | c[¬B][B][L] = c[¬B][B]} if c[¬B][B] ≠ ∅ 

c[¬B][(if B) L] = 

Undefined 

otherwise 

• This update is undefined, since the presupposition fails 



Contrast When Antecedent is Denied: Subjunctives 

(8) Bob never danced. If Bob had danced, Leland would 

have danced. 

(8 ′ ) ¬B. (if ✁B) L 

⎧ 

⎨ {w ∈ c f | c f [¬B][✁B][L] = c f [¬B][✁B]} if c f [¬B][✁B] ≠ ∅ 

c f [¬B][(if ✁B) L] = 

⎩ 

Undefined 

otherwise 

• This update will (probably) be defined 

• ✁ can reach outside c, so presupposition is weakened 

by subjunctive antecedent 

• Weakened but not eliminated: requires antecedent to 

be f-visible, i.e. f must find some φ world 





Summary 

1 A uniform semantics for two kinds of conditionals 

• Same semantics for (if φ) ψ 

• Difference resides in subjunctive antecedent: ✁α 

2 Embodies Stalnaker’s Distinction: 

• And so explains subjunctive suggestion and contrast 

w/denying antecedent 

3 Embodies Stalnaker’s Distinction by pursuing the 

Modal Hypothesis 

• This explains the correlation between fake past and 

subjunctive/indicative 


The New Analysis 

Import-Export 

(15) a. If Adam had come, then there would have been a 

fight if Bob had come 

b. (if ✁A) ((if ✁B) F) 

(16) a. If Adam had come and Bob had come, there 

would have been a fight 

a. (if ✁A ∧ ✁B) F 

Import-Export 

(if ✁α 1 ) ((if ✁α 2 ) ψ) 

 

(if ✁α 1 ∧ ✁α 2 ) ψ 

• Invalid on Lewis-Stalnaker semantics 

• Valid on present analysis 








Towards Another Phenomena 

(17) a. If Bob had danced or Sarah had sang, Andy 

would have cried 

b. So, if Bob had danced, Andy would have cried, 

and if Sarah had sang, Andy would have cried 

(18) a. (if (✁B ∨ ✁S)) C 

b. (if ✁B) C ∧ (if ✁S) C 


(if (✁α ∨ ✁β)) ψ ((if ✁α) ψ) ∧ ((if ✁β) ψ) 

• Invalid on Lewis-Stalnaker semantics 

• Valid on present analysis 

• Conditional semantics from Starr (2010: Ch.2) has 

more bells and whistles 

• One of them is relevant here: stacks of contexts, rather 

than just contexts 

• Starr (2010: Ch.2) uses this allows to give a uniform 

analysis of interrogative and conditional if 

• Here, it will allow me to analyze various phenomena 

involving sequences of conditionals 




Hypothetical Additions 

Logical Tourism 

• Information is not only taken for granted in 

conversation and inquiry 

• Agents routinely entertain certain enrichments of the 

information they are taking for granted 

• Acts like supposition introduce these enrichments; the 

speech acts which follow may exploit what’s 

entertained in addition to what’s taken for granted 

• Real virtuosity comes in the ways that what’s 

entertained can be related to what’s accepted 


States of Inquiry 

States of Inquiry and Hypothetical Change 

Proposal: represent hypothetical change via states of inquiry 

Let s be a state of inquiry — state for short 

s 

c 

−−→ 

state 

change 

−−−−→ 

s ↓ p 

c 

c[p] 

Figure: Supposing p 

1 s = 〈c〉 — nothing 

entertained 

2 s ↓ p = 〈c, 〈c[p]〉〉 — c[p] is 

entertained 

3 Call s ↓ p Subordination 

(Related proposal: Kaufmann 2000) 




Another Operation 

For Suppositional Discourse and Reasoning 


Decomposing the Conditional Further 

A Sequence of Stack Updates 

s[(if ✁α) ψ] = (s ↓ ✁α) ↑ ψ 

Conclusion: s ↑ q 

Relates what’s entertained to what’s accepted via an 

entailment test. Let s = 〈 c, 〈c[p]〉〉: 

• If c[p] (what’s entertained) entails q, c remains as is 

• Otherwise, something actually contradictory has been 

proposed, i.e. we are brought to: 〈∅, 〈c〉〉 

s 

c 

↓ ✁α 

c f 

c f [⊳α] 

c f [⊳α][ψ] 

↑ ψ 

c ′ f 

s ↑ q = 〈{w ∈ c | c[p] q}〉, 〈c[p][q]〉 

c ′ f 

= {w ∈ c f | c f [✁α] ψ} 

= c f or ∅ 




Successful Updates 

Create Subordinate Contexts 


Reverse Sobel Sequences 

Another Application 

c f 

c f [⊳α][ψ] 

Modal Subordination: Roberts (1989) 

(19) a. Your cabin wasn’t raided by a 

coyote. 

b. But if a coyote had raided your 

cabin, it would’ve eaten your 

dinner. 

c. It would’ve eaten your meat first. 

• (19) is interpreted against subordinate context 

• Specifically: 〈c f [✁R][E]〉 ↑ F 

• Which context sentences are interpreted against is 

determined by discourse connections like anaphora 

von Fintel (2001); Gillies (2007) 

(20) a. If Sophie had gone to the parade, she would have 

seen Pedro dance 

b. But of course, if Sophie had gone to the parade 

and been stuck behind someone tall, she would 

not have seen Pedro dance 

(21) a. If Sophie had gone to the parade and been stuck 

behind someone tall, she would not have seen 

Pedro dance 

b. # But of course, if Sophie had gone to the parade, 

she would have seen Pedro dance 





The Explanation in Symbols 

(22) a. (if ✁S) P 

b. (if ✁S ∧ ✁T) ¬P 

(23) a. (if ✁S ∧ ✁T) ¬P 

b. # (if ✁S) P 

• Both s[(22a)][(22b)] and s[(22a)] ↑ (22b) are identical 

• By contrast s[(23a)][(23b)] and s[(23a)] ↑ (23b) are not 

• First tests: c f [✁S] P 

• Second tests: c f [✁S][✁T][¬P][✁S] P 

• This test fails! 

• There is a strong bias towards the second, inconsistent 

discourse structure; hard to defeat, not impossible 



Are Sometimes Good (Moss to appear: §4) 

(Context: speaker wants to indirectly convey the 

information that Mary would have turned down a marriage 

proposal from John.) 

(24) a. If John had proposed to Mary and she had said 

yes, he would have been really happy 

b. But if John had proposed to Mary, he would have 

been really unhappy 

• This discourse structure: s[(24a)][(24b)] 

• Not: s[(24a)] ↑ (24b) 

• This an issue for strict semantic accounts (von Fintel 

2001; Gillies 2007), but not mine 





Anaphora Correlates w/Inconsistency 

(25) Although John was seriously considering a proposal to 

Mary, he didn’t end up proposing. He never even 

bought a ring. 

(26) a. If John had offered Mary an engagement ring and 

she had said yes, he would have been really happy 

b. # But if John had offered it to Mary, he would 

have been really unhappy 

• Parallel to Moss’s case, but w/anaphora from from 

first conditional to second 

• Anaphora forces second conditional to be interpreted 

against the subordinate state created by the first 

• Hence inconsistency 



Summary 

1 Independently motivated apparatus explains 

inconsistency of reverse Sobel sequences 

• Needed for analysis of interrogative/conditional if 

• Needed for modal subordination 

2 More flexible than von Fintel (2001); Gillies (2007) 

3 But explains correlation with anaphoric dependence 

unlike Moss (to appear) 




The Theory 

Summary 


1 Unlike Stalnaker’s, this theory gives a unified 

explanation of: 

• The contrast with denied antecedents 

• The subjunctive suggestion 

• Correlation between fake past and 

subjunctive/indicative 

2 This theory delivers a better logic of indicatives & 

subjunctives than Stalnaker’s 

• Import-Export, Disjunctive Antecedents 

3 It also offers a competitive analysis of reverse Sobel 

sequences that links them to anaphoricity 

Thanks! 




References I 


References II 

Bittner, M (2010). ‘Conditionals as Attitude Reports.’ Ms. Rutgers University, 

URL http://www.rci.rutgers.edu/~mbittner/pdf%20files%20for%20web/ 

bittner10_jos.pdf. 

von Fintel, K (2001). ‘Counterfactuals in a Dynamic Context.’ In 

M Kenstowicz (ed.), Ken Hale: a Life in Language, 123–152. Cambridge, 

Massachusetts: The MIT Press. URL 

http://mit.edu/fintel/www/conditional.pdf. 

Gillies, A (2007). ‘Counterfactual Scorekeeping.’ Linguistics & Philosophy, 

30(3): 329–360. URL 

http://rci.rutgers.edu/~thony/counterfactualscorekeeping_landp.pdf. 

Gillies, A (2009). ‘On Truth-Conditions for If (but Not Quite Only If ).’ 

Philosophical Review, 118(3): 325–349. URL http: 

//rci.rutgers.edu/~thony/truth-conditions-if-phil-review-2009.pdf. 

Heim, I (1982). The Semantics of Definite and Indefinite Noun Phrases. Ph.D. 

thesis, Linguistics Department, University of Massachusetts, Amherst, 

Massachusetts. 

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Linguistic Inquiry, 31(2): 231–270. 

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233–55. 

Kaufmann, S (2000). ‘Dynamic Context Management.’ In M Faller, 

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171–188. Stanford, CA: CSLI Publications. 

Lewis, DK (1979). ‘Scorekeeping in a Language Game.’ Journal of Philosophical 

Logic, 8(3): 339–359. 

Lyons, J (1977). Semantics, vol. 2. Cambridge, England: Cambridge University 

Press. 

Moss, S (to appear). ‘On the Pragmatics of Counterfactuals.’ Noûs. URL 

http://www-personal.umich.edu/~ssmoss/counterfactuals.pdf. 

Pratt, VR (1976). ‘Semantical Considerations on Floyd-Hoare Logic.’ In 

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Science, 109–121. 

Roberts, C (1989). ‘Modal Subordination and Pronominal Anaphora in 

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Stalnaker, RC (1968). ‘A Theory of Conditionals.’ In N Rescher (ed.), Studies 

in Logical Theory, 98–112. Oxford: Basil Blackwell Publishers. 




References III 

Stalnaker, RC (1975). ‘Indicative Conditionals.’ Philosophia, 5: 269–286. Page 

references to reprint in Stalnaker (1999). 

Stalnaker, RC (1978). ‘Assertion.’ In P Cole (ed.), Syntax and Semantics 9: 

Pragmatics, 315–332. New York: Academic Press. References to reprint in 

Stalnaker (1999). 

Stalnaker, RC (1999). Context and Content: Essays on Intentionality in Speech 

and Thought. Oxford: Oxford University Press. 

Stalnaker, RC (2005). ‘Conditional Propositions and Conditional Assertions.’ In 

J Gajewski, V Hacquard, B Nickel & S Yalcin (eds.), New Work on 

Modality, vol. 51 of MIT Working Papers in Linguistics. Cambridge, MA: 

MITWPL. 

Starr, WB (2010). Conditionals, Meaning and Mood. Ph.D. thesis, Rutgers 

University, New Brunswick, NJ. URL 

http://williamstarr.net/research/dissertation.pdf. 

Veltman, F (1996). ‘Defaults in Update Semantics.’ Journal of Philosophical 

Logic, 25(3): 221–261. URL 

http://www.pgrim.org/philosophersannual/xix/velt/index.htm.

A Uniform Theory of Conditionals: Beyond Stalnaker - Will Starr

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